Inferring functional connections between neurons

Comparison of derivative-based and correlation-based methods to estimate effective connectivity in neural networks

Inferring and understanding the underlying connectivity structure of a system solely from the observed activity of its constituent components is a challenge in many areas of science. In neuroscience, techniques for estimating connectivity are paramount when attempting to understand the network structure of neural systems from their recorded activity patterns. To date, no universally accepted method exists for the inference of effective connectivity, which describes how the activity of a neural node mechanistically affects the activity of other nodes. Here, focussing on purely excitatory networks of small to intermediate size and continuous node dynamics, we provide a systematic comparison of different approaches for estimating effective connectivity. Starting with the Hopf neuron model in conjunction with known ground truth structural connectivity, we reconstruct the system's connectivity matrix using a variety of algorithms. We show that, in sparse non-linear networks with delays, combining a lagged-cross-correlation (LCC) approach with a recently published derivative-based covariance analysis method provides the most reliable estimation of the known ground truth connectivity matrix. We outline how the parameters of the Hopf model, including those controlling the bifurcation, noise, and delay distribution, affect this result. We also show that in linear networks, LCC has comparable performance to a method based on transfer entropy, at a drastically lower computational cost. We highlight that LCC works best for small sparse networks, and show how performance decreases in larger and less sparse networks. Applying the method to linear dynamics without time delays, we find that it does not outperform derivative-based methods. We comment on this finding in light of recent theoretical results for such systems. Employing the Hopf model, we then use the estimated structural connectivity matrix as the basis for a forward simulation of the system dynamics, in order to recreate the observed node activity patterns. We show that, under certain conditions, the best method, LCC, results in higher trace-to-trace correlations than derivative-based methods for sparse noise-driven systems. Finally, we apply the LCC method to empirical biological data. Choosing a suitable threshold for binarization, we reconstruct the structural connectivity of a subset of the nervous system of the nematode C. elegans. We show that the computationally simple LCC method performs better than another recently published, computationally more expensive reservoir computing-based method. We apply different methods to this dataset and find that they all lead to similar performances. Our results show that a comparatively simple method can be used to reliably estimate directed effective connectivity in sparse neural systems in the presence of spatio-temporal delays and noise. We provide concrete suggestions for the estimation of effective connectivity in a scenario common in biological research, where only neuronal activity of a small set of neurons, but not connectivity or single-neuron and synapse dynamics, are known.

Charactering Neural Spiking Activity Evoked by Acupuncture Through Coupling Generalized Linear Model

Acupuncturing the ST36 acupoint can evoke a responding activity in the spinal dorsal root ganglia and generate spikes. In order to identify the responding mechanism of different acupuncture manipulations, in this paper the spike history of neurons is taken as the starting point and the coupling generalized linear model is adopted to encode the neuronal spiking activity evoked by different acupuncture manipulations. Then, maximum likelihood estimation is used to fit the model parameters and estimate the coupling parameters of stimulus, the self-coupling parameters of the neuron's own spike history and the cross-coupling parameters of other neurons' spike history. We use simulation data to test the estimation algorithm's effectiveness and analyze the main factors that evoke neuronal responding activity. Finally, we use the coupling generalized linear model to encode neuronal spiking activity evoked by two acupuncture manipulations, and estimate the coupling parameters of stimulus, the self-coupling parameters and the cross-coupling parameters. The results show that in acupuncture experiments, acupuncture stimulus is the inducing factor of neuronal spiking activity, and the cross-coupling of other neurons' spike history is the main factor of neuronal spiking activity. Additionally, the higher the amplitude of the neuronal spiking waveform, the greater the cross-coupling parameter. This lays a theoretical foundation for the scientific application of acupuncture therapy.

Inference of monosynaptic connections from parallel spike trains: A review

This article presents a mini-review about the progress in inferring monosynaptic connections from spike trains of multiple neurons over the past twenty years. First, we explain a variety of meanings of "neuronal connectivity" in different research areas of neuroscience, such as structural connectivity, monosynaptic connectivity, and functional connectivity. Among these, we focus on the methods used to infer the monosynaptic connectivity from spike data. We then summarize the inference methods based on two main approaches, i.e., correlation-based and model-based approaches. Finally, we describe available source codes for connectivity inference and future challenges. Although inference will never be perfect, the accuracy of identifying the monosynaptic connections has improved dramatically in recent years due to continuous efforts.

NSF DARE-Transforming modeling in neurorehabilitation: Four threads for catalyzing progress

We present an overview of the Conference on Transformative Opportunities for Modeling in Neurorehabilitation held in March 2023. It was supported by the Disability and Rehabilitation Engineering (DARE) program from the National Science Foundation's Engineering Biology and Health Cluster. The conference brought together experts and trainees from around the world to discuss critical questions, challenges, and opportunities at the intersection of computational modeling and neurorehabilitation to understand, optimize, and improve clinical translation of neurorehabilitation. We organized the conference around four key, relevant, and promising Focus Areas for modeling: Adaptation & Plasticity, Personalization, Human-Device Interactions, and Modeling 'In-the-Wild'. We identified four common threads across the Focus Areas that, if addressed, can catalyze progress in the short, medium, and long terms. These were: (i) the need to capture and curate appropriate and useful data necessary to develop, validate, and deploy useful computational models (ii) the need to create multi-scale models that span the personalization spectrum from individuals to populations, and from cellular to behavioral levels (iii) the need for algorithms that extract as much information from available data, while requiring as little data as possible from each client (iv) the insistence on leveraging readily available sensors and data systems to push model-driven treatments from the lab, and into the clinic, home, workplace, and community. The conference archive can be found at (dare2023.usc.edu). These topics are also extended by three perspective papers prepared by trainees and junior faculty, clinician researchers, and federal funding agency representatives who attended the conference.

Causal connectivity measures for pulse-output network reconstruction: Analysis and applications

The causal connectivity of a network is often inferred to understand network function. It is arguably acknowledged that the inferred causal connectivity relies on the causality measure one applies, and it may differ from the network's underlying structural connectivity. However, the interpretation of causal connectivity remains to be fully clarified, in particular, how causal connectivity depends on causality measures and how causal connectivity relates to structural connectivity. Here, we focus on nonlinear networks with pulse signals as measured output, e.g., neural networks with spike output, and address the above issues based on four commonly utilized causality measures, i.e., time-delayed correlation coefficient, time-delayed mutual information, Granger causality, and transfer entropy. We theoretically show how these causality measures are related to one another when applied to pulse signals. Taking a simulated Hodgkin-Huxley network and a real mouse brain network as two illustrative examples, we further verify the quantitative relations among the four causality measures and demonstrate that the causal connectivity inferred by any of the four well coincides with the underlying network structural connectivity, therefore illustrating a direct link between the causal and structural connectivity. We stress that the structural connectivity of pulse-output networks can be reconstructed pairwise without conditioning on the global information of all other nodes in a network, thus circumventing the curse of dimensionality. Our framework provides a practical and effective approach for pulse-output network reconstruction.

Statistically inferred neuronal connections in subsampled neural networks strongly correlate with spike train covariances

Statistically inferred neuronal connections from observed spike train data are often skewed from ground truth by factors such as model mismatch, unobserved neurons, and limited data. Spike train covariances, sometimes referred to as "functional connections," are often used as a proxy for the connections between pairs of neurons, but reflect statistical relationships between neurons, not anatomical connections. Moreover, covariances are not causal: spiking activity is correlated in both the past and the future, whereas neurons respond only to synaptic inputs in the past. Connections inferred by maximum likelihood inference, however, can be constrained to be causal. However, we show in this work that the inferred connections in spontaneously active networks modeled by stochastic leaky integrate-and-fire networks strongly correlate with the covariances between neurons, and may reflect noncausal relationships, when many neurons are unobserved or when neurons are weakly coupled. This phenomenon occurs across different network structures, including random networks and balanced excitatory-inhibitory networks. We use a combination of simulations and a mean-field analysis with fluctuation corrections to elucidate the relationships between spike train covariances, inferred synaptic filters, and ground-truth connections in partially observed networks.

Inferring causal connectivity from pairwise recordings and optogenetics

To understand the neural mechanisms underlying brain function, neuroscientists aim to quantify causal interactions between neurons, for instance by perturbing the activity of neuron A and measuring the effect on neuron B. Recently, manipulating neuron activity using light-sensitive opsins, optogenetics, has increased the specificity of neural perturbation. However, using widefield optogenetic interventions, multiple neurons are usually perturbed, producing a confound-any of the stimulated neurons can have affected the postsynaptic neuron making it challenging to discern which neurons produced the causal effect. Here, we show how such confounds produce large biases in interpretations. We explain how confounding can be reduced by combining instrumental variables (IV) and difference in differences (DiD) techniques from econometrics. Combined, these methods can estimate (causal) effective connectivity by exploiting the weak, approximately random signal resulting from the interaction between stimulation and the absolute refractory period of the neuron. In simulated neural networks, we find that estimates using ideas from IV and DiD outperform naïve techniques suggesting that methods from causal inference can be useful to disentangle neural interactions in the brain.

Measurable fields-to-spike causality and its dependence on cortical layer and area

Distinct dynamics in different cortical layers are apparent in neuronal and local field potential (LFP) patterns, yet their associations in the context of laminar processing have been sparingly analyzed. Here, we study the laminar organization of spike-field causal flow within and across visual (V4) and frontal areas (PFC) of monkeys performing a visual task. Using an event-based quantification of LFPs and a directed information estimator, we found area and frequency specificity in the laminar organization of spike-field causal connectivity. Gamma bursts (40-80 Hz) in the superficial layers of V4 largely drove intralaminar spiking. These gamma influences also fed forward up the cortical hierarchy to modulate laminar spiking in PFC. In PFC, the direction of intralaminar information flow was from spikes → fields where these influences dually controlled top-down and bottom-up processing. Our results, enabled by innovative methodologies, emphasize the complexities of spike-field causal interactions amongst multiple brain areas and behavior.

Resolving Non-identifiability Mitigates Bias in Models of Neural Tuning and Functional Coupling

In the brain, all neurons are driven by the activity of other neurons, some of which maybe simultaneously recorded, but most are not. As such, models of neuronal activity need to account for simultaneously recorded neurons and the influences of unmeasured neurons. This can be done through inclusion of model terms for observed external variables (e.g., tuning to stimuli) as well as terms for latent sources of variability. Determining the influence of groups of neurons on each other relative to other influences is important to understand brain functioning. The parameters of statistical models fit to data are commonly used to gain insight into the relative importance of those influences. Scientific interpretation of models hinge upon unbiased parameter estimates. However, evaluation of biased inference is rarely performed and sources of bias are poorly understood. Through extensive numerical study and analytic calculation, we show that common inference procedures and models are typically biased. We demonstrate that accurate parameter selection before estimation resolves model non-identifiability and mitigates bias. In diverse neurophysiology data sets, we found that contributions of coupling to other neurons are often overestimated while tuning to exogenous variables are underestimated in common methods. We explain heterogeneity in observed biases across data sets in terms of data statistics. Finally, counter to common intuition, we found that model non-identifiability contributes to bias, not variance, making it a particularly insidious form of statistical error. Together, our results identify the causes of statistical biases in common models of neural data, provide inference procedures to mitigate that bias, and reveal and explain the impact of those biases in diverse neural data sets.

Insulin and fluoxetine produce opposite actions on lateral septal nucleus-infralimbic region connection responsivity

Some diabetes patients develop depression, the main treatment for which is antidepressants. Pharmacological interactions between insulin and antidepressants (e.g., fluoxetine) are controversial in the literature. Some authors reported hypoglycemic actions of fluoxetine, whereas others reported antidepressant-like actions. In healthy rats, insulin produces an antidespair-like action in rats through an increase in locomotor and exploratory activity, but differences in actions of insulin and fluoxetine on neuronal activity are unknown. The present study evaluated Wistar healthy rats that were treated with saline, insulin, fluoxetine, or fluoxetine + insulin for 3 days (short-term) or 21 days (long-term). The model consisted of electrical stimulation of the lateral septal nucleus (LSN) while we performed single-unit extracellular response recordings in the prelimbic cortex (PL) and infralimbic cortex (IL) subregions of the medial prefrontal cortex (mPFC). Stimulation of the LSN produced an initial brief excitatory paucisynaptic response and then a long-lasting inhibitory afterdischarge in the PL and IL. Treatment with saline and fluoxetine, but not insulin, minimally affected the paucisynaptic response. Differences were found in LSN-IL responsivity. The inhibitory afterdischarge was clearly enhanced in the long-term fluoxetine group but not by insulin alone or fluoxetine + insulin. These findings suggest that insulin produces some actions that are opposite to fluoxetine on LSN-mPFC connection responsivity, with no synergistic actions between the actions of insulin and fluoxetine.

Reconstruction of sparse recurrent connectivity and inputs from the nonlinear dynamics of neuronal networks

Reconstructing the recurrent structural connectivity of neuronal networks is a challenge crucial to address in characterizing neuronal computations. While directly measuring the detailed connectivity structure is generally prohibitive for large networks, we develop a novel framework for reverse-engineering large-scale recurrent network connectivity matrices from neuronal dynamics by utilizing the widespread sparsity of neuronal connections. We derive a linear input-output mapping that underlies the irregular dynamics of a model network composed of both excitatory and inhibitory integrate-and-fire neurons with pulse coupling, thereby relating network inputs to evoked neuronal activity. Using this embedded mapping and experimentally feasible measurements of the firing rate as well as voltage dynamics in response to a relatively small ensemble of random input stimuli, we efficiently reconstruct the recurrent network connectivity via compressive sensing techniques. Through analogous analysis, we then recover high dimensional natural stimuli from evoked neuronal network dynamics over a short time horizon. This work provides a generalizable methodology for rapidly recovering sparse neuronal network data and underlines the natural role of sparsity in facilitating the efficient encoding of network data in neuronal dynamics.

Statistical perspective on functional and causal neural connectomics: The Time-Aware PC algorithm

The representation of the flow of information between neurons in the brain based on their activity is termed the causal functional connectome. Such representation incorporates the dynamic nature of neuronal activity and causal interactions between them. In contrast to connectome, the causal functional connectome is not directly observed and needs to be inferred from neural time series. A popular statistical framework for inferring causal connectivity from observations is the directed probabilistic graphical modeling. Its common formulation is not suitable for neural time series since it was developed for variables with independent and identically distributed static samples. In this work, we propose to model and estimate the causal functional connectivity from neural time series using a novel approach that adapts directed probabilistic graphical modeling to the time series scenario. In particular, we develop the Time-Aware PC (TPC) algorithm for estimating the causal functional connectivity, which adapts the PC algorithm-a state-of-the-art method for statistical causal inference. We show that the model outcome of TPC has the properties of reflecting causality of neural interactions such as being non-parametric, exhibits the directed Markov property in a time-series setting, and is predictive of the consequence of counterfactual interventions on the time series. We demonstrate the utility of the methodology to obtain the causal functional connectome for several datasets including simulations, benchmark datasets, and recent multi-array electro-physiological recordings from the mouse visual cortex.

Stop and think: Additional time supports monitoring processes in young children

When children evaluate their certainty, monitoring is often inaccurate. Even though young children struggle to estimate their confidence, existing research shows that monitoring skills are developing earlier than expected. Using a paired associates learning task with integrated monitoring, we implemented a time window to—"Stop and Think"—before children generated their answers and evaluated their confidence in the chosen response. Results show that kindergarten and second grade children in the—"Stop and Think"—condition have higher monitoring accuracy than the control group. Implementing a time window thus seems to support children in their evaluation of different certainty levels. Relating individual differences in independently measured inhibitory control skills revealed a correlation between monitoring and inhibition for kindergarteners.

Dynamical differential covariance recovers directional network structure in multiscale neural systems

Investigating neural interactions is essential to understanding the neural basis of behavior. Many statistical methods have been used for analyzing neural activity, but estimating the direction of network interactions correctly and efficiently remains a difficult problem. Here, we derive dynamical differential covariance (DDC), a method based on dynamical network models that detects directional interactions with low bias and high noise tolerance under nonstationarity conditions. Moreover, DDC scales well with the number of recording sites and the computation required is comparable to that needed for covariance. DDC was validated and compared favorably with other methods on networks with false positive motifs and multiscale neural simulations where the ground-truth connectivity was known. When applied to recordings of resting-state functional magnetic resonance imaging (rs-fMRI), DDC consistently detected regional interactions with strong structural connectivity in over 1,000 individual subjects obtained by diffusion MRI (dMRI). DDC is a promising family of methods for estimating connectivity that can be generalized to a wide range of dynamical models and recording techniques and to other applications where system identification is needed.

Functional Implications of Dale's Law in Balanced Neuronal Network Dynamics and Decision Making

The notion that a neuron transmits the same set of neurotransmitters at all of its post-synaptic connections, typically known as Dale's law, is well supported throughout the majority of the brain and is assumed in almost all theoretical studies investigating the mechanisms for computation in neuronal networks. Dale's law has numerous functional implications in fundamental sensory processing and decision-making tasks, and it plays a key role in the current understanding of the structure-function relationship in the brain. However, since exceptions to Dale's law have been discovered for certain neurons and because other biological systems with complex network structure incorporate individual units that send both positive and negative feedback signals, we investigate the functional implications of network model dynamics that violate Dale's law by allowing each neuron to send out both excitatory and inhibitory signals to its neighbors. We show how balanced network dynamics, in which large excitatory and inhibitory inputs are dynamically adjusted such that input fluctuations produce irregular firing events, are theoretically preserved for a single population of neurons violating Dale's law. We further leverage this single-population network model in the context of two competing pools of neurons to demonstrate that effective decision-making dynamics are also produced, agreeing with experimental observations from honeybee dynamics in selecting a food source and artificial neural networks trained in optimal selection. Through direct comparison with the classical two-population balanced neuronal network, we argue that the one-population network demonstrates more robust balanced activity for systems with less computational units, such as honeybee colonies, whereas the two-population network exhibits a more rapid response to temporal variations in network inputs, as required by the brain. We expect this study will shed light on the role of neurons violating Dale's law found in experiment as well as shared design principles across biological systems that perform complex computations.

Functional connectivity of fMRI using differential covariance predicts structural connectivity and behavioral reaction times

Recordings from resting state functional Magnetic Resonance Imaging (rs-fMRI) reflect the influence of pathways between brain areas. A wide range of methods have been proposed to measure this functional connectivity (FC), but the lack of “ground truth” has made it difficult to systematically validate them. Most measures of FC produce connectivity estimates that are symmetrical between brain areas. Differential covariance (dCov) is an algorithm for analyzing FC with directed graph edges. When we applied dCov to rs-fMRI recordings from the human connectome project (HCP) and anesthetized mice, dCov-FC accurately identified strong cortical connections from diffusion Magnetic Resonance Imaging (dMRI) in individual humans and viral tract tracing in mice. In addition, those HCP subjects whose dCov-FCs were more integrated, as assessed by a graph-theoretic measure, tended to have shorter reaction times in several behavioral tests. Thus, dCov-FC was able to identify anatomically verified connectivity that yielded measures of brain integration significantly correlated with behavior.

Efficient spline regression for neural spiking data

Point process generalized linear models (GLMs) provide a powerful tool for characterizing the coding properties of neural populations. Spline basis functions are often used in point process GLMs, when the relationship between the spiking and driving signals are nonlinear, but common choices for the structure of these spline bases often lead to loss of statistical power and numerical instability when the signals that influence spiking are bounded above or below. In particular, history dependent spike train models often suffer these issues at times immediately following a previous spike. This can make inferences related to refractoriness and bursting activity more challenging. Here, we propose a modified set of spline basis functions that assumes a flat derivative at the endpoints and show that this limits the uncertainty and numerical issues associated with cardinal splines. We illustrate the application of this modified basis to the problem of simultaneously estimating the place field and history dependent properties of a set of neurons from the CA1 region of rat hippocampus, and compare it with the other commonly used basis functions. We have made code available in MATLAB to implement spike train regression using these modified basis functions.

A convolutional neural network for estimating synaptic connectivity from spike trains

The recent increase in reliable, simultaneous high channel count extracellular recordings is exciting for physiologists and theoreticians because it offers the possibility of reconstructing the underlying neuronal circuits. We recently presented a method of inferring this circuit connectivity from neuronal spike trains by applying the generalized linear model to cross-correlograms. Although the algorithm can do a good job of circuit reconstruction, the parameters need to be carefully tuned for each individual dataset. Here we present another method using a Convolutional Neural Network for Estimating synaptic Connectivity from spike trains. After adaptation to huge amounts of simulated data, this method robustly captures the specific feature of monosynaptic impact in a noisy cross-correlogram. There are no user-adjustable parameters. With this new method, we have constructed diagrams of neuronal circuits recorded in several cortical areas of monkeys.

Inferring thalamocortical monosynaptic connectivity in vivo

As the tools to simultaneously record electrophysiological signals from large numbers of neurons within and across brain regions become increasingly available, this opens up for the first time the possibility of establishing the details of causal relationships between monosynaptically connected neurons and the patterns of neural activation that underlie perception and behavior. Although recorded activity across synaptically connected neurons has served as the cornerstone for much of what we know about synaptic transmission and plasticity, this has largely been relegated to ex vivo preparations that enable precise targeting under relatively well-controlled conditions. Analogous studies in vivo, where image-guided targeting is often not yet possible, rely on indirect, data-driven measures, and as a result such studies have been sparse and the dependence upon important experimental parameters has not been well studied. Here, using in vivo extracellular single-unit recordings in the topographically aligned rodent thalamocortical pathway, we sought to establish a general experimental and computational framework for inferring synaptic connectivity. Specifically, attacking this problem within a statistical signal detection framework utilizing experimentally recorded data in the ventral-posterior medial (VPm) region of the thalamus and the homologous region in layer 4 of primary somatosensory cortex (S1) revealed a trade-off between network activity levels needed for the data-driven inference and synchronization of nearby neurons within the population that results in masking of synaptic relationships. Here, we provide a framework for establishing connectivity in multisite, multielectrode recordings based on statistical inference, setting the stage for large-scale assessment of synaptic connectivity within and across brain structures.NEW & NOTEWORTHY Despite the fact that all brain function relies on the long-range transfer of information across different regions, the tools enabling us to measure connectivity across brain structures are lacking. Here, we provide a statistical framework for identifying and assessing potential monosynaptic connectivity across neuronal circuits from population spiking activity that generalizes to large-scale recording technologies that will help us to better understand the signaling within networks that underlies perception and behavior.

Improved inference in coupling, encoding, and decoding models and its consequence for neuroscientific interpretation

BACKGROUND

A central goal of systems neuroscience is to understand the relationships amongst constituent units in neural populations, and their modulation by external factors, using high-dimensional and stochastic neural recordings. Parametric statistical models (e.g., coupling, encoding, and decoding models), play an instrumental role in accomplishing this goal. However, extracting conclusions from a parametric model requires that it is fit using an inference algorithm capable of selecting the correct parameters and properly estimating their values. Traditional approaches to parameter inference have been shown to suffer from failures in both selection and estimation. The recent development of algorithms that ameliorate these deficiencies raises the question of whether past work relying on such inference procedures have produced inaccurate systems neuroscience models, thereby impairing their interpretation.

NEW METHOD

We used algorithms based on Union of Intersections, a statistical inference framework based on stability principles, capable of improved selection and estimation.

COMPARISON

We fit functional coupling, encoding, and decoding models across a battery of neural datasets using both UoI and baseline inference procedures (e.g., ℓ₁-penalized GLMs), and compared the structure of their fitted parameters.

RESULTS

Across recording modality, brain region, and task, we found that UoI inferred models with increased sparsity, improved stability, and qualitatively different parameter distributions, while maintaining predictive performance. We obtained highly sparse functional coupling networks with substantially different community structure, more parsimonious encoding models, and decoding models that relied on fewer single-units.

CONCLUSIONS

Together, these results demonstrate that improved parameter inference, achieved via UoI, reshapes interpretation in diverse neuroscience contexts.

Model-based detection of putative synaptic connections from spike recordings with latency and type constraints

Detecting synaptic connections using large-scale extracellular spike recordings is a difficult statistical problem. Here, we develop an extension of a generalized linear model that explicitly separates fast synaptic effects and slow background fluctuations in cross-correlograms between pairs of neurons while incorporating circuit properties learned from the whole network. This model outperforms two previously developed synapse detection methods in the simulated networks and recovers plausible connections from hundreds of neurons in in vitro multielectrode array data.

Rethinking brain-wide interactions through multi-region 'network of networks' models

The neural control of behavior is distributed across many functionally and anatomically distinct brain regions even in small nervous systems. While classical neuroscience models treated these regions as a set of hierarchically isolated nodes, the brain comprises a recurrently interconnected network in which each region is intimately modulated by many others. Uncovering these interactions is now possible through experimental techniques that access large neural populations from many brain regions simultaneously. Harnessing these large-scale datasets, however, requires new theoretical approaches. Here, we review recent work to understand brain-wide interactions using multi-region 'network of networks' models and discuss how they can guide future experiments. We also emphasize the importance of multi-region recordings, and posit that studying individual components in isolation will be insufficient to understand the neural basis of behavior.

Inferring neural information flow from spiking data

The brain can be regarded as an information processing system in which neurons store and propagate information about external stimuli and internal processes. Therefore, estimating interactions between neural activity at the cellular scale has significant implications in understanding how neuronal circuits encode and communicate information across brain areas to generate behavior. While the number of simultaneously recorded neurons is growing exponentially, current methods relying only on pairwise statistical dependencies still suffer from a number of conceptual and technical challenges that preclude experimental breakthroughs describing neural information flows. In this review, we examine the evolution of the field over the years, starting from descriptive statistics to model-based and model-free approaches. Then, we discuss in detail the Granger Causality framework, which includes many popular state-of-the-art methods and we highlight some of its limitations from a conceptual and practical estimation perspective. Finally, we discuss directions for future research, including the development of theoretical information flow models and the use of dimensionality reduction techniques to extract relevant interactions from large-scale recording datasets.

Differential Covariance: A New Method to Estimate Functional Connectivity in fMRI

Measuring functional connectivity from fMRI recordings is important in understanding processing in cortical networks. However, because the brain's connection pattern is complex, currently used methods are prone to producing false functional connections. We introduce differential covariance analysis, a new method that uses derivatives of the signal for estimating functional connectivity. We generated neural activities from dynamical causal modeling and a neural network of Hodgkin-Huxley neurons and then converted them to hemodynamic signals using the forward balloon model. The simulated fMRI signals, together with the ground-truth connectivity pattern, were used to benchmark our method with other commonly used methods. Differential covariance achieved better results in complex network simulations. This new method opens an alternative way to estimate functional connectivity.

Modeling the Short-Term Dynamics of in Vivo Excitatory Spike Transmission

Information transmission in neural networks is influenced by both short-term synaptic plasticity (STP) as well as nonsynaptic factors, such as after-hyperpolarization currents and changes in excitability. Although these effects have been widely characterized in vitro using intracellular recordings, how they interact in vivo is unclear. Here, we develop a statistical model of the short-term dynamics of spike transmission that aims to disentangle the contributions of synaptic and nonsynaptic effects based only on observed presynaptic and postsynaptic spiking. The model includes a dynamic functional connection with short-term plasticity as well as effects due to the recent history of postsynaptic spiking and slow changes in postsynaptic excitability. Using paired spike recordings, we find that the model accurately describes the short-term dynamics of in vivo spike transmission at a diverse set of identified and putative excitatory synapses, including a pair of connected neurons within thalamus in mouse, a thalamocortical connection in a female rabbit, and an auditory brainstem synapse in a female gerbil. We illustrate the utility of this modeling approach by showing how the spike transmission patterns captured by the model may be sufficient to account for stimulus-dependent differences in spike transmission in the auditory brainstem (endbulb of Held). Finally, we apply this model to large-scale multielectrode recordings to illustrate how such an approach has the potential to reveal cell type-specific differences in spike transmission in vivo Although STP parameters estimated from ongoing presynaptic and postsynaptic spiking are highly uncertain, our results are partially consistent with previous intracellular observations in these synapses.SIGNIFICANCE STATEMENT Although synaptic dynamics have been extensively studied and modeled using intracellular recordings of postsynaptic currents and potentials, inferring synaptic effects from extracellular spiking is challenging. Whether or not a synaptic current contributes to postsynaptic spiking depends not only on the amplitude of the current, but also on many other factors, including the activity of other, typically unobserved, synapses, the overall excitability of the postsynaptic neuron, and how recently the postsynaptic neuron has spiked. Here, we developed a model that, using only observations of presynaptic and postsynaptic spiking, aims to describe the dynamics of in vivo spike transmission by modeling both short-term synaptic plasticity (STP) and nonsynaptic effects. This approach may provide a novel description of fast, structured changes in spike transmission.

Recurrent circuit dynamics underlie persistent activity in the macaque frontoparietal network

During delayed oculomotor response tasks, neurons in the lateral intraparietal area (LIP) and the frontal eye fields (FEF) exhibit persistent activity that reflects the active maintenance of behaviorally relevant information. Despite many computational models of the mechanisms of persistent activity, there is a lack of circuit-level data from the primate to inform the theories. To fill this gap, we simultaneously recorded ensembles of neurons in both LIP and FEF while macaques performed a memory-guided saccade task. A population encoding model revealed strong and symmetric long-timescale recurrent excitation between LIP and FEF. Unexpectedly, LIP exhibited stronger local functional connectivity than FEF, and many neurons in LIP had longer network and intrinsic timescales. The differences in connectivity could be explained by the strength of recurrent dynamics in attractor networks. These findings reveal reciprocal multi-area circuit dynamics in the frontoparietal network during persistent activity and lay the groundwork for quantitative comparisons to theoretical models.

Long-term stability of cortical population dynamics underlying consistent behavior

Animals readily execute learned behaviors in a consistent manner over long periods of time, and yet no equally stable neural correlate has been demonstrated. How does the cortex achieve this stable control? Using the sensorimotor system as a model of cortical processing, we investigated the hypothesis that the dynamics of neural latent activity, which captures the dominant co-variation patterns within the neural population, must be preserved across time. We recorded from populations of neurons in premotor, primary motor and somatosensory cortices as monkeys performed a reaching task, for up to 2 years. Intriguingly, despite a steady turnover in the recorded neurons, the low-dimensional latent dynamics remained stable. The stability allowed reliable decoding of behavioral features for the entire timespan, while fixed decoders based directly on the recorded neural activity degraded substantially. We posit that stable latent cortical dynamics within the manifold are the fundamental building blocks underlying consistent behavioral execution.

Compressive Sensing Inference of Neuronal Network Connectivity in Balanced Neuronal Dynamics

Determining the structure of a network is of central importance to understanding its function in both neuroscience and applied mathematics. However, recovering the structural connectivity of neuronal networks remains a fundamental challenge both theoretically and experimentally. While neuronal networks operate in certain dynamical regimes, which may influence their connectivity reconstruction, there is widespread experimental evidence of a balanced neuronal operating state in which strong excitatory and inhibitory inputs are dynamically adjusted such that neuronal voltages primarily remain near resting potential. Utilizing the dynamics of model neurons in such a balanced regime in conjunction with the ubiquitous sparse connectivity structure of neuronal networks, we develop a compressive sensing theoretical framework for efficiently reconstructing network connections by measuring individual neuronal activity in response to a relatively small ensemble of random stimuli injected over a short time scale. By tuning the network dynamical regime, we determine that the highest fidelity reconstructions are achievable in the balanced state. We hypothesize the balanced dynamics observed in vivo may therefore be a result of evolutionary selection for optimal information encoding and expect the methodology developed to be generalizable for alternative model networks as well as experimental paradigms.

Reconstructing neuronal circuitry from parallel spike trains

State-of-the-art techniques allow researchers to record large numbers of spike trains in parallel for many hours. With enough such data, we should be able to infer the connectivity among neurons. Here we develop a method for reconstructing neuronal circuitry by applying a generalized linear model (GLM) to spike cross-correlations. Our method estimates connections between neurons in units of postsynaptic potentials and the amount of spike recordings needed to verify connections. The performance of inference is optimized by counting the estimation errors using synthetic data. This method is superior to other established methods in correctly estimating connectivity. By applying our method to rat hippocampal data, we show that the types of estimated connections match the results inferred from other physiological cues. Thus our method provides the means to build a circuit diagram from recorded spike trains, thereby providing a basis for elucidating the differences in information processing in different brain regions.

Current techniques have enabled the simultaneous collection of spike train data from large numbers of neurons. Here, the authors report a method to infer the underlying neural circuit connectivity diagram based on a generalized linear model applied to spike cross-correlations between neurons.

Model-Based Inference of Synaptic Transmission

Synaptic computation is believed to underlie many forms of animal behavior. A correct identification of synaptic transmission properties is thus crucial for a better understanding of how the brain processes information, stores memories and learns. Recently, a number of new statistical methods for inferring synaptic transmission parameters have been introduced. Here we review and contrast these developments, with a focus on methods aimed at inferring both synaptic release statistics and synaptic dynamics. Furthermore, based on recent proposals we discuss how such methods can be applied to data across different levels of investigation: from intracellular paired experiments to in vivo network-wide recordings. Overall, these developments open the window to reliably estimating synaptic parameters in behaving animals.

In vitro validation of in silico identified inhibitory interactions

BACKGROUND

Understanding how neuronal signals propagate in local network is an important step in understanding information processing. As a result, spike trains recorded with multi-electrode arrays (MEAs) have been widely used to study the function of neural networks. Studying the dynamics of neuronal networks requires the identification of both excitatory and inhibitory connections. The detection of excitatory relationships can robustly be inferred by characterizing the statistical relationships of neural spike trains. However, the identification of inhibitory relationships is more difficult: distinguishing endogenous low firing rates from active inhibition is not obvious.

NEW METHOD

In this paper, we propose an in silico interventional procedure that makes predictions about the effect of stimulating or inhibiting single neurons on other neurons, and thereby gives the ability to accurately identify inhibitory effects.

COMPARISON

To experimentally test these predictions, we have developed a Neural Circuit Probe (NCP) that delivers drugs transiently and reversibly on individually identified neurons to assess their contributions to the neural circuit behavior.

RESULTS

Using the NCP, putative inhibitory connections identified by the in silico procedure were validated through in vitro interventional experiments.

CONCLUSIONS

Together, these results demonstrate how detailed microcircuitry can be inferred from statistical models derived from neurophysiology data.

Multi-Input, Multi-Output Neuronal Mode Network Approach to Modeling the Encoding Dynamics and Functional Connectivity of Neural Systems

This letter proposes a novel method, multi-input, multi-output neuronal mode network (MIMO-NMN), for modeling encoding dynamics and functional connectivity in neural ensembles such as the hippocampus. Compared with conventional approaches such as the Volterra-Wiener model, linear-nonlinear-cascade (LNC) model, and generalized linear model (GLM), the NMN has several advantages in terms of estimation accuracy, model interpretation, and functional connectivity analysis. We point out the limitations of current neural spike modeling methods, especially the estimation biases caused by the imbalanced class problem when the number of zeros is significantly larger than ones in the spike data. We use synthetic data to test the performance of NMN with a comparison of the traditional methods, and the results indicate the NMN approach could reduce the imbalanced class problem and achieve better predictions. Subsequently, we apply the MIMO-NMN method to analyze data from the human hippocampus. The results indicate that the MIMO-NMN method is a promising approach to modeling neural dynamics and analyzing functional connectivity of multi-neuronal data.

Medial temporal lobe functional connectivity predicts stimulation-induced theta power

Focal electrical stimulation of the brain incites a cascade of neural activity that propagates from the stimulated region to both nearby and remote areas, offering the potential to control the activity of brain networks. Understanding how exogenous electrical signals perturb such networks in humans is key to its clinical translation. To investigate this, we applied electrical stimulation to subregions of the medial temporal lobe in 26 neurosurgical patients fitted with indwelling electrodes. Networks of low-frequency (5–13 Hz) spectral coherence predicted stimulation-evoked increases in theta (5–8 Hz) power, particularly when stimulation was applied in or adjacent to white matter. Stimulation tended to decrease power in the high-frequency broadband (HFB; 50–200 Hz) range, and these modulations were correlated with HFB-based networks in a subset of subjects. Our results demonstrate that functional connectivity is predictive of causal changes in the brain, capturing evoked activity across brain regions and frequency bands.

Direct electrical brain stimulation can induce widespread changes in neural activity, offering a means to modulate network-wide activity and treat disease. Here, the authors show that the low-frequency functional connectivity profile of a stimulation target predicts where induced theta activity occurs.

Predicting how and when hidden neurons skew measured synaptic interactions

A major obstacle to understanding neural coding and computation is the fact that experimental recordings typically sample only a small fraction of the neurons in a circuit. Measured neural properties are skewed by interactions between recorded neurons and the “hidden” portion of the network. To properly interpret neural data and determine how biological structure gives rise to neural circuit function, we thus need a better understanding of the relationships between measured effective neural properties and the true underlying physiological properties. Here, we focus on how the effective spatiotemporal dynamics of the synaptic interactions between neurons are reshaped by coupling to unobserved neurons. We find that the effective interactions from a pre-synaptic neuron r′ to a post-synaptic neuron r can be decomposed into a sum of the true interaction from r′ to r plus corrections from every directed path from r′ to r through unobserved neurons. Importantly, the resulting formula reveals when the hidden units have—or do not have—major effects on reshaping the interactions among observed neurons. As a particular example of interest, we derive a formula for the impact of hidden units in random networks with “strong” coupling—connection weights that scale with 1/N, where N is the network size, precisely the scaling observed in recent experiments. With this quantitative relationship between measured and true interactions, we can study how network properties shape effective interactions, which properties are relevant for neural computations, and how to manipulate effective interactions.

No experiment in neuroscience can record from more than a tiny fraction of the total number of neurons present in a circuit. This severely complicates measurement of a network’s true properties, as unobserved neurons skew measurements away from what would be measured if all neurons were observed. For example, the measured post-synaptic response of a neuron to a spike from a particular pre-synaptic neuron incorporates direct connections between the two neurons as well as the effect of any number of indirect connections, including through unobserved neurons. To understand how measured quantities are distorted by unobserved neurons, we calculate a general relationship between measured “effective” synaptic interactions and the ground-truth interactions in the network. This allows us to identify conditions under which hidden neurons substantially alter measured interactions. Moreover, it provides a foundation for future work on manipulating effective interactions between neurons to better understand and potentially alter circuit function—or dysfunction.

A Neural Population Mechanism for Rapid Learning

Long-term learning of language, mathematics, and motor skills likely requires cortical plasticity, but behavior often requires much faster changes, sometimes even after single errors. Here, we propose one neural mechanism to rapidly develop new motor output without altering the functional connectivity within or between cortical areas. We tested cortico-cortical models relating the activity of hundreds of neurons in the premotor (PMd) and primary motor (M1) cortices throughout adaptation to reaching movement perturbations. We found a signature of learning in the "output-null" subspace of PMd with respect to M1 reflecting the ability of premotor cortex to alter preparatory activity without directly influencing M1. The output-null subspace planning activity evolved with adaptation, yet the "output-potent" mapping that captures information sent to M1 was preserved. Our results illustrate a population-level cortical mechanism to progressively adjust the output from one brain area to its downstream structures that could be exploited for rapid behavioral adaptation.

Linear-nonlinear-time-warp-poisson models of neural activity

Prominent models of spike trains assume only one source of variability - stochastic (Poisson) spiking - when stimuli and behavior are fixed. However, spike trains may also reflect variability due to internal processes such as planning. For example, we can plan a movement at one point in time and execute it at some arbitrary later time. Neurons involved in planning may thus share an underlying time course that is not precisely locked to the actual movement. Here we combine the standard Linear-Nonlinear-Poisson (LNP) model with Dynamic Time Warping (DTW) to account for shared temporal variability. When applied to recordings from macaque premotor cortex, we find that time warping considerably improves predictions of neural activity. We suggest that such temporal variability is a widespread phenomenon in the brain which should be modeled.

Multiple Approaches to the Investigation of Cell Assembly in Memory Research-Present and Future

In this review article we focus on research methodologies for detecting the actual activity of cell assemblies, which are populations of functionally connected neurons that encode information in the brain. We introduce and discuss traditional and novel experimental methods and those currently in development and briefly discuss their advantages and disadvantages for the detection of cell-assembly activity. First, we introduce the electrophysiological method, i.e., multineuronal recording, and review former and recent examples of studies showing models of dynamic coding by cell assemblies in behaving rodents and monkeys. We also discuss how the firing correlation of two neurons reflects the firing synchrony among the numerous surrounding neurons that constitute cell assemblies. Second, we review the recent outstanding studies that used the novel method of optogenetics to show causal relationships between cell-assembly activity and behavioral change. Third, we review the most recently developed method of live-cell imaging, which facilitates the simultaneous observation of firings of a large number of neurons in behaving rodents. Currently, all these available methods have both advantages and disadvantages, and no single measurement method can directly and precisely detect the actual activity of cell assemblies. The best strategy is to combine the available methods and utilize each of their advantages with the technique of operant conditioning of multiple-task behaviors in animals and, if necessary, with brain-machine interface technology to verify the accuracy of neural information detected as cell-assembly activity.

Active learning of cortical connectivity from two-photon imaging data

Understanding how groups of neurons interact within a network is a fundamental question in system neuroscience. Instead of passively observing the ongoing activity of a network, we can typically perturb its activity, either by external sensory stimulation or directly via techniques such as two-photon optogenetics. A natural question is how to use such perturbations to identify the connectivity of the network efficiently. Here we introduce a method to infer sparse connectivity graphs from in-vivo, two-photon imaging of population activity in response to external stimuli. A novel aspect of the work is the introduction of a recommended distribution, incrementally learned from the data, to optimally refine the inferred network. Unlike existing system identification techniques, this “active learning” method automatically focuses its attention on key undiscovered areas of the network, instead of targeting global uncertainty indicators like parameter variance. We show how active learning leads to faster inference while, at the same time, provides confidence intervals for the network parameters. We present simulations on artificial small-world networks to validate the methods and apply the method to real data. Analysis of frequency of motifs recovered show that cortical networks are consistent with a small-world topology model.

A Copula-Based Granger Causality Measure for the Analysis of Neural Spike Train Data

In systems neuroscience, it is becoming increasingly common to record the activity of hundreds of neurons simultaneously via electrode arrays. The ability to accurately measure the causal interactions among multiple neurons in the brain is crucial to understanding how neurons work in concert to generate specific brain functions. The development of new statistical methods for assessing causal influence between spike trains is still an active field of neuroscience research. Here, we suggest a copula-based Granger causality measure for the analysis of neural spike train data. This method is built upon our recent work on copula Granger causality for the analysis of continuous-valued time series by extending it to point-process neural spike train data. The proposed method is therefore able to reveal nonlinear and high-order causality in the spike trains while retaining all the computational advantages such as model-free, efficient estimation, and variability assessment of Granger causality. The performance of our algorithm can be further boosted with time-reversed data. Our method performed well on extensive simulations, and was then demonstrated on neural activity simultaneously recorded from primary visual cortex of a monkey performing a contour detection task.

Reconstructing the functional connectivity of multiple spike trains using Hawkes models

BACKGROUND

Statistical models that predict neuron spike occurrence from the earlier spiking activity of the whole recorded network are promising tools to reconstruct functional connectivity graphs. Some of the previously used methods are in the general statistical framework of the multivariate Hawkes processes. However, they usually require a huge amount of data, some prior knowledge about the recorded network, and/or may produce an increasing number of spikes along time during simulation.

NEW METHOD

Here, we present a method, based on least-square estimators and LASSO penalty criteria, for a particular class of Hawkes processes that can be used for simulation.

RESULTS

Testing our method on small networks modeled with Leaky Integrate and Fire demonstrated that it efficiently detects both excitatory and inhibitory connections. The few errors that occasionally occur with complex networks including common inputs, weak and chained connections, can be discarded based on objective criteria.

COMPARISON WITH EXISTING METHODS

With respect to other existing methods, the present one allows to reconstruct functional connectivity of small networks without prior knowledge of their properties or architecture, using an experimentally realistic amount of data.

CONCLUSIONS

The present method is robust, stable, and can be used on a personal computer as a routine procedure to infer connectivity graphs and generate simulation models from simultaneous spike train recordings.

MEA Viewer: A high-performance interactive application for visualizing electrophysiological data

Action potentials can be recorded extracellularly from hundreds of neurons simultaneously with multi-electrode arrays. These can typically have as many as 120 or more electrodes. The brief duration of action potentials requires a high sampling frequency to reliably capture each waveform. The resulting raw data files are therefore large and difficult to visualize with traditional plotting tools. Common approaches to deal with the difficulties of data display, such as extracting spike times and performing spike train analysis, are useful in many contexts but they also significantly reduce data dimensionality. The use of tools which minimize data processing enable the development of heuristic perspective of experimental results. Here we introduce MEA Viewer, a high-performance open source application for the direct visualization of multi-channel electrophysiological data. MEA Viewer includes several high-performance visualizations, including an easily navigable overview of recorded extracellular action potentials from all data channels overlaid with spike timestamp data and an interactive raster plot. MEA Viewer can also display the two dimensional extent of action potential propagation in single neurons by signal averaging extracellular action potentials (eAPs) from single neurons detected on multiple electrodes. This view extracts and displays eAP timing information and eAP waveforms that are otherwise below the spike detection threshold. This entirely new method of using MEAs opens up novel research applications for medium density arrays. MEA Viewer is licensed under the General Public License version 3, GPLv3, and is available at http://github.com/dbridges/mea-tools.

Functional coupling networks inferred from prefrontal cortex activity show experience-related effective plasticity

Functional coupling networks are widely used to characterize collective patterns of activity in neural populations. Here, we ask whether functional couplings reflect the subtle changes, such as in physiological interactions, believed to take place during learning. We infer functional network models reproducing the spiking activity of simultaneously recorded neurons in prefrontal cortex (PFC) of rats, during the performance of a cross-modal rule shift task (task epoch), and during preceding and following sleep epochs. A large-scale study of the 96 recorded sessions allows us to detect, in about 20% of sessions, effective plasticity between the sleep epochs. These coupling modifications are correlated with the coupling values in the task epoch, and are supported by a small subset of the recorded neurons, which we identify by means of an automatized procedure. These potentiated groups increase their coativation frequency in the spiking data between the two sleep epochs, and, hence, participate to putative experience-related cell assemblies. Study of the reactivation dynamics of the potentiated groups suggests a possible connection with behavioral learning. Reactivation is largely driven by hippocampal ripple events when the rule is not yet learned, and may be much more autonomous, and presumably sustained by the potentiated PFC network, when learning is consolidated.

Cell assemblies coding for memories are widely believed to emerge through synaptic modification resulting from learning, yet their identification from activity is very arduous. We propose a functional-connectivity-based approach to identify experience-related cell assemblies from multielectrode recordings in vivo, and apply it to the prefrontal cortex activity of rats recorded during a task epoch and the preceding and following sleep epochs. We infer functional couplings between the recorded cells in each epoch. Comparisons of the functional coupling networks across the epochs allow us to identify effective potentiation between the two sleep epochs. The neurons supporting these potentiated interactions strongly coactivate during the task and subsequent sleep epochs, but not in the preceding sleep, and, hence, presumably belong to an experience-related cell assembly. Study of the reactivation of this assembly in response to hippocampal ripple inputs suggests possible relations between the stage of behavorial learning and memory consolidation mechanisms.

Estimating short-term synaptic plasticity from pre- and postsynaptic spiking

Short-term synaptic plasticity (STP) critically affects the processing of information in neuronal circuits by reversibly changing the effective strength of connections between neurons on time scales from milliseconds to a few seconds. STP is traditionally studied using intracellular recordings of postsynaptic potentials or currents evoked by presynaptic spikes. However, STP also affects the statistics of postsynaptic spikes. Here we present two model-based approaches for estimating synaptic weights and short-term plasticity from pre- and postsynaptic spike observations alone. We extend a generalized linear model (GLM) that predicts postsynaptic spiking as a function of the observed pre- and postsynaptic spikes and allow the connection strength (coupling term in the GLM) to vary as a function of time based on the history of presynaptic spikes. Our first model assumes that STP follows a Tsodyks-Markram description of vesicle depletion and recovery. In a second model, we introduce a functional description of STP where we estimate the coupling term as a biophysically unrestrained function of the presynaptic inter-spike intervals. To validate the models, we test the accuracy of STP estimation using the spiking of pre- and postsynaptic neurons with known synaptic dynamics. We first test our models using the responses of layer 2/3 pyramidal neurons to simulated presynaptic input with different types of STP, and then use simulated spike trains to examine the effects of spike-frequency adaptation, stochastic vesicle release, spike sorting errors, and common input. We find that, using only spike observations, both model-based methods can accurately reconstruct the time-varying synaptic weights of presynaptic inputs for different types of STP. Our models also capture the differences in postsynaptic spike responses to presynaptic spikes following short vs long inter-spike intervals, similar to results reported for thalamocortical connections. These models may thus be useful tools for characterizing short-term plasticity from multi-electrode spike recordings in vivo.

Inferring structural connectivity using Ising couplings in models of neuronal networks

Functional connectivity metrics have been widely used to infer the underlying structural connectivity in neuronal networks. Maximum entropy based Ising models have been suggested to discount the effect of indirect interactions and give good results in inferring the true anatomical connections. However, no benchmarking is currently available to assess the performance of Ising couplings against other functional connectivity metrics in the microscopic scale of neuronal networks through a wide set of network conditions and network structures. In this paper, we study the performance of the Ising model couplings to infer the synaptic connectivity in in silico networks of neurons and compare its performance against partial and cross-correlations for different correlation levels, firing rates, network sizes, network densities, and topologies. Our results show that the relative performance amongst the three functional connectivity metrics depends primarily on the network correlation levels. Ising couplings detected the most structural links at very weak network correlation levels, and partial correlations outperformed Ising couplings and cross-correlations at strong correlation levels. The result was consistent across varying firing rates, network sizes, and topologies. The findings of this paper serve as a guide in choosing the right functional connectivity tool to reconstruct the structural connectivity.

Differential Covariance: A New Class of Methods to Estimate Sparse Connectivity from Neural Recordings

With our ability to record more neurons simultaneously, making sense of these data is a challenge. Functional connectivity is one popular way to study the relationship of multiple neural signals. Correlation-based methods are a set of currently well-used techniques for functional connectivity estimation. However, due to explaining away and unobserved common inputs (Stevenson, Rebesco, Miller, & Körding, 2008 ), they produce spurious connections. The general linear model (GLM), which models spike trains as Poisson processes (Okatan, Wilson, & Brown, 2005 ; Truccolo, Eden, Fellows, Donoghue, & Brown, 2005 ; Pillow et al., 2008 ), avoids these confounds. We develop here a new class of methods by using differential signals based on simulated intracellular voltage recordings. It is equivalent to a regularized AR(2) model. We also expand the method to simulated local field potential recordings and calcium imaging. In all of our simulated data, the differential covariance-based methods achieved performance better than or similar to the GLM method and required fewer data samples. This new class of methods provides alternative ways to analyze neural signals.

Robustness and versatility of a nonlinear interdependence method for directional coupling detection from spike trains

The detection of directional couplings between dynamics based on measured spike trains is a crucial problem in the understanding of many different systems. In particular, in neuroscience it is important to assess the connectivity between neurons. One of the approaches that can estimate directional coupling from the analysis of point processes is the nonlinear interdependence measure L. Although its efficacy has already been demonstrated, it still needs to be tested under more challenging and realistic conditions prior to an application to real data. Thus, in this paper we use the Hindmarsh-Rose model system to test the method in the presence of noise and for different spiking regimes. We also examine the influence of different parameters and spike train distances. Our results show that the measure L is versatile and robust to various types of noise, and thus suitable for application to experimental data.

Reconstructing networks of pulse-coupled oscillators from spike trains

We present an approach for reconstructing networks of pulse-coupled neuronlike oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases are instantaneously reset by incoming pulses. Using an iterative procedure, we recover the properties of all nodes, namely their phase response curves and natural frequencies, as well as strengths of all directed connections.